Umberger and Huselius found the net only 2:16 apart late in the game, erasing a 3-2 deficit and handing the Blue Jackets the comeback win.
Umberger. who also had two assists, tied it with less than 7 minutes remaining when he slipped the puck through the legs of a defender and fired a shot past Nikolai Khabibulin from the left circle.
Huselius then put the Jackets ahead with 4 minutes left on a wrist shot from the slot.
Steve Mason earned the victory after allowing three goals on 26 shots.
The Oilers lost despite two goals from Magnus Paajarvi.
Dustin Penner also scored and Khabibulin ended with 30 saves.